Before I knew I was pregnant, I drank alcohol occasionally. I noticed that I got drunk much quicker than normal. Is this related to my pregnancy and will it go away after birth?

Real tough. I hope you have stopped drinking now. There is no answer to your question as the effect of alcohol on pregnant women will never be done.
Yes. Your metabolism and liver do change quickly when you become pregnant and this could have affected your tolerance to alcohol. Can't say if it will go back to normal.